On the Hodge structure of varieties of tangent lines for cubic surfaces
Atsushi Ikeda (Tokyo Denki-Pavia)
Aula Beltrami - Wednesday, May 18, 2016 h.16:00
Abstract. For a hypersurface in projective space, we consider the set of lines which are tangent to the hypersurface with a higher multiplicity.
This set forms a subvariety in the Grassmannian of lines, and we call it the variety of tangent lines.
First I will introduce some general properties of the varieties of tangent lines.
Next we restrict to the case for a nonsingular cubic surface.
Then, the variety of tangent lines is an algebraic surface of general type.
I will explain the geometry of rational curves on it and give a description of the Hodge structure.
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